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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum gain and absorption in the two-color three-level V atom: a dressed-state picture

Doron Braunstein, R. Shuker

Published Jan 6, 1999• 1 citation
Publisher

Abstract

Light amplification without population inversion and absorption with inversion driven by quantum coherent interferences in a closed three level V-type system is studied from the point of view of two color dressed state basis. Approximate analytic time dependent solutions, for coherences and population distribution are derived, and compared with full numerical solutions. Steady state quantities are also calculated, and the conditions under which the system exhibits gain with and without inversion, in the dressed state representation are derived. It is found that for a weak probe laser field light amplification without inversion may occur, for a range of system parameters, in both the bare and the dressed state representations.

DOI
10.1117/12.335830

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Light amplification without population inversion and absorption with inversion driven by quantum coherent interferences in a closed three level V-type system is studied from the point of view of two color dressed state basis. Approximate analytic time dependent solutions, for coherences and population distribution are derived, and compared with full numerical solutions. Steady state quantities are also calculated, and the conditions under which the system exhibits gain with and without inversion, in the dressed state representation are derived. It is found that for a weak probe laser field light amplification without inversion may occur, for a range of system parameters, in both the bare and the dressed state representations.
Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.
Summary form only given.A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.
The steady-state populations and the absorption spectrum of a V-type three-level atom driven by a strong coherent field and a weak stochastic one simultaneously are investigated. The population inversion in bare-state and dressed-state bases can happen significantly due to the effect of the stochastic field. A relation between the level gap of both atomic excited states and the Rabi frequency is found to decide in which excited state the population is larger than in another one for the same frequency detuning δ between the coherent and the stochastic fields. The line profiles of the absorption spectrum are strongly dependent on the frequency detuning δ. Different lineshapes such as a sharp emission peak (gain), an absorption peak or a dispersion-like peak can be exhibited at the line centre for different δ. Asymmetrical spectral features and line narrowing can be reached by adjusting δ and the Rabi frequency. Probe gain in sidebands can occur due to the unbalanced population distribution in dressed states.
We analyze transient properties of light amplification without population inversion (LWI) in a closed three-level @sV -type system and study the system evolution from transient LWI into steady-state LWI. From the time evolution of the atomic coherence and population distribution with and without an incoherent pump field, we elucidate the light amplification mechanism and derive the conditions under which the @sV system exhibits LWI in any state basis. We derive analytical solution for the steady-state LWI and discuss other mechanisms of light amplification such as stimulated Raman scattering and population inversion in the dressed states. \textcopyright{} 1996 The American Physical Society.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.